CMC Spheres in the Heisenberg Group

Abstract

We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture. We also focus our attention on the sub-Riemannian limit.

Keywords

• constant mean curvature surfaces
• heisenberg group
• isoperimetric problem
• 49q10
• 53a10